Scientific Notation Calculator
Convert numbers to scientific notation and e-notation, with steps.
Loading calculator…
What Is Scientific Notation?
Scientific notation is a short way to write very large or very small numbers. A number is written as a coefficient between 1 and 10, times 10 to a power. For example, 5,000 is 5 × 10³. The number 0.00045 is 4.5 × 10⁻⁴.
The coefficient must be at least 1 and less than 10. So 12 × 10³ is not scientific notation, but 1.2 × 10⁴ is. The exponent tells you how many places the decimal point moved, and in which direction.
Scientists use this form because their numbers are extreme. The speed of light is 3 × 10⁸ metres per second. The mass of an electron is about 9.11 × 10⁻³¹ kilograms. Writing these out in full would take dozens of digits and invite mistakes.
How to Convert to Scientific Notation
Converting a number takes two steps:
- Move the decimal point until only one non-zero digit is to its left. For 45,000, move the point 4 places left to get 4.5.
- Count the places you moved. That count is the exponent. If you moved the point left, the exponent is positive. If you moved it right, the exponent is negative.
Examples: 45,000 becomes 4.5 × 10⁴. 0.00045 becomes 4.5 × 10⁻⁴. 7 becomes 7 × 10⁰. To go back, move the decimal point the other way: 4.5 × 10⁻⁴ means move the point 4 places left from 4.5, giving 0.00045.
The decimal to fraction calculator is the companion tool for this one: it turns decimals into exact fractions, while this page turns them into powers of ten.
E-Notation: What Calculators Show
When a calculator shows 3.2e5, it means 3.2 × 10⁵. The letter e stands for "times 10 to the power of". This is called e-notation, and it is the form computers and calculators use because they cannot print a superscript.
Some common e-notation values: 1e3 is 1,000. 2.5e-2 is 0.025. 6.02e23 is Avogadro's number, about 602,000,000,000,000,000,000,000. If you see e-notation on a screen, just read the part after the e as the exponent of 10.
Be careful not to mix up e-notation with the number e (about 2.718), which is a different thing. In 3.2e5, the e is only a short way of writing "times 10 to the power of".
Multiplying and Dividing in Scientific Notation
Scientific notation makes big-number arithmetic easy. To multiply, multiply the coefficients and add the exponents: (2 × 10³) × (3 × 10²) = 6 × 10⁵. To divide, divide the coefficients and subtract the exponents: (6 × 10⁵) ÷ (2 × 10²) = 3 × 10³.
To add or subtract, first make the exponents equal. For 3 × 10⁴ + 2 × 10³, rewrite 2 × 10³ as 0.2 × 10⁴, then add the coefficients: 3.2 × 10⁴. If your answer has a coefficient of 10 or more, fix it by moving the decimal point once more and raising the exponent by one.
These rules are why science and engineering classes insist on scientific notation. A problem with 23-digit numbers becomes a problem with one-digit coefficients and small exponents.
Practice With Our Free Tool
Use the scientific notation calculator above to check your homework. Enter any number and see its scientific form, e-notation and full form at once. For graphing work, the function graphing calculator plots the functions behind these numbers. Everything is free, with no download and no sign-up.
Specialized Graphing Tools
Frequently Asked Questions
Scientific notation is a short way to write very large or very small numbers. A number is written as a coefficient between 1 and 10, times 10 to a power. For example, 5,000 is 5 times 10 to the power of 3, written as 5 x 10^3.
Move the decimal point until only one non-zero digit is to its left. Count how many places you moved it. That count is the exponent. If you moved the point left, the exponent is positive. If you moved it right, the exponent is negative. For 0.00045, move the point 4 places right, so the answer is 4.5 x 10^-4.
E-notation is the short form used by calculators and computers. The letter e stands for times 10 to the power of. So 3.2 x 10^5 is written as 3.2e5, and 4.5 x 10^-4 is written as 4.5e-4. It means exactly the same thing as scientific notation.
Scientists use it for numbers that are too big or too small to write out easily. The speed of light is 3 x 10^8 metres per second. The mass of an electron is about 9.11 x 10^-31 kilograms. Writing these out in full would take dozens of digits and invite mistakes.
Yes. The scientific notation calculator is free to use online. There is no download and no sign-up. You can convert as many numbers as you want, right in your browser.